INRIA-GAMMA3 Contribution 2st AIAA Sonic-Boom workshop€¦ · Scope of the presentation Inviscid...

INRIA-GAMMA3 Contribution2st AIAA Sonic-Boom workshop

Adrien Loseille 1, Loıc Frazza1 and Frederic Alauzet1

1GAMMA3 TeamINRIA, France

Scope of the presentation

Inviscid cases:Jaxa Wing-Body provided-unstructuredC25D provided-unstructured and adaptive grids

Partially done (not presented) :Axie Euler, provided-unstructured tet gridsC25D RANS, powered and flow-through on provided tet grids

General context

Tetrahedral meshes onlyParallel computation 12 cores (24 threads), Xeon E7 @ 3.7Ghz, 512GbError estimates

multi-scale (Lp) interpolation error Mach numbergoal-oriented (GO) approximation error pressure observation

Adrien Loseille , Loıc Frazza and Frederic Alauzet ( GAMMA3 Team INRIA, France )2st AIAA SB Workshop 2 / 24

Wolf Flow Solver [Alauzet & Loseille, JCP 2012], [Menier et Al., AIAA 2014]

Conservative Euler equations

Numerical resolution: Mixed-Element-Volume Method (MEV)I vertex-centered: low complexityI edge-based formulation with upwind element: 1D splittingI HLLC approximate Riemann solverI MUSCL type method: inexpensive high-order extensionsI Van Albada limiterI Properties:

F ConservativeF Positivity preservingF Monotone: TVD

Time advancing: Implicit SGS scheme


Jaxa case: Flow solver convergence (6.5M)

Residual computed over the maximum residual of the simulationAfter a reduction of 5 orders of magnitude : freezing of the limiters (tofinish convergence)


Jaxa case: signature convergences (R/L=0.85)

For embedded meshes, a mesh with 3N represents a change in edgelength of 0.7 for 3N with respect to 1 for N


Jaxa case: Uncertainty estimates (6M, R/L=0.85)

Non linear correction, based on source term estimate F(Wh)[Loseille et al., AIAA 2014]





Jaxa case: signature convergences (R/L=2.55)

For embedded meshes, a mesh with 3N represents a change in edgelength of 0.7 for 3N with respect to 1 for N









=⇒ Use of mesh adaptation to reduce and equi-distribute error barsnorm-oriented mesh adaptation


C25D inviscid flow-through: Flow solver convergence(3.4M)


C25D inviscid flow-through: Flow solver convergence(3.4M)


Anisotropic Error estimates

Interpolation error controlled:Observation solution field:

Mach number : uh =⇒ control of ‖Rh(uh)− ΠhRh(uh)‖L2(Ω)

Anisotropic goal-orientedObservation functional:

j(U) =

∫S

(p − p∞)2 =⇒ control of |j(U)− jh(Uh)|

S is the symmetry plane with z < 0

Local remeshing : Feflo.a [Loseille et al., JCAD 2016]

surface and volume remeshingmetric-based for anisotropy


C25D inviscid flow-through

Multi-scale mesh adaptation:

16 adaptations, ≈ 13 076 solver iterations in total

# vertices # tetrahedra mean ratio mean quotient1 946 918 11 093 526 10 975 529 916 32 726 736 18 297

12 953 271 77 497 813 18 32527 644 454 166 148 147 19 400

Adjoint-based mesh adaptation:

12 adaptations, ≈ 8 176 solver iterations in total

# vertices # tetrahedra mean ratio mean quotient1 555 516 8 680 173 8 613 112 225 17 894 815 14 1975 915 408 34 553 239 17 2213

11 736 061 68 985 939 46 5713


C25D inviscid flow-through : Adjoint functional# vertices # tetrahedra mean ratio mean quotient1 555 516 8 680 173 8 613 112 225 17 894 815 14 1975 915 408 34 553 239 17 2213

11 736 061 68 985 939 46 5713


C25D : Tailored mesh convergence







For all R/L:+ Accurate and low dissipation- No mesh convergence observed for computed meshes (≤ 27M)


C25D : Lp-based mesh convergence







- Solutions dissipated for large R/L- DoF lost in the upper part of the domains (stronger shocks)- No mesh convergence observed for computed meshes (≤ 27M)


C25D : Adjoint-based mesh convergence







+ Mesh convergence observed for most of the shocks (6M)-(11M) for R/L=1- Signal accurate for Φ = 0, needs to change functional for additional Φ


C25D : Comparisons Iso-DoF (≈ 13M)






C25D : Comparisons Iso-DoF (Best Effort)







Large discrepancy in the second part of signalHypothesis: maybe due to non linear (complex) effects


C25D inviscid flow-through : Pressure field (x=30)

Taylored (27M) LP (27M)

Best effort meshes



LP (27M) GO (11M)

Best effort meshes



Taylored( 27M) LP(27M)

Best effort meshes



LP (27M) GO (11M)

Best effort meshes



Taylored (27M) LP (27M)

Best effort meshes



LP (27M) GO (11M)

Best effort meshes


C25D inviscid flow-through : Pressure field

Symmetry

Taylored (27M) GO (6M)


C25D inviscid flow-through : Pressure fieldSymmetry

GO GO

IssuesTaylored mesh are hard to compete with but :Impact of the refinement in the uniform part for taylored


C25D inviscid flow-through : Conclusion

C25D geometryHighly non linear flow features: vortices, shock/shock/vortices interaction

Mesh convergenceNot obtained for tailored and LP with more around 27 M verticesAlmost achieved for the adjoint (in the symmetry plane only)

Taylored approachHard to compete with : low dissipation in the propagationAny requirements on the accuracy in the uniform field ?

Going furtherAdapt only the inner cylinder domaineLP tailored approach with Hessian dissipation in the z > 0Push the methods to reach asymptotic convergence O(107 − 108)vertices ...


General conclusion

Improvements over the 1st workshopfrom 1 Million vertices meshes to 27 Million for the 2nd workshopRANS cases run while not computed for the 1st workshopResidual computations improvements for flow with shocks

On-going work/Current limitationsLinear system resolution for the adjoint system, currently limited to 10Million vertices then we do not reach convergenceDistributed parallelization of the flow solverRANS adaptationUse of a corrector to asses solution convergence and drive adaptivityUse metric-aligned mesh generation


General conclusion

Metric-aligned mesh


General conclusion

Metric-aligned mesh


General conclusionImprovements over the 1st workshop

from 1 million vertices meshes to 27 million for the 2nd workshopRANS cases run while not computed for the 1st workshopResidual computations improvements for flow with shocks

On-going work/Current limitationsLinear system resolution for the adjoint system, currently limited to10 million vertices then we do not reach convergenceDistributed parallelization of the flow solverRANS adaptationUse of a corrector to asses solution convergence and drive adaptivityUse metric-aligned mesh generation

More detailsError estimates, adaptive strategies and uncertainty computations,monday afternoon sessionLow boom session, Dallas 6, Monday afternoon


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INRIA-GAMMA3 Contribution 2st AIAA Sonic-Boom workshop€¦ · Scope of the presentation Inviscid...

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